Modelling of Non-Stationary Spatial Structure Using Parametric Radial Basis Deformations

Perrin, Olivier; Monestiez, Pascal

doi:10.1007/978-94-015-9297-0_15

Cited by 26 publications

(27 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Stein (2007, 2008), Castruccio and Stein (2013) and Castruccio and Genton (2016) advocated a spectral approach that provides flexible non-stationary covariance models on the sphere. Alternatively, Sampson and Guttorp (1992), Perrin and Monestiez (1999), Schmidt and O'Hagan (2003) and Anderes and Stein (2008) created nonstationary processes by smooth deformations of isotropic random fields. Bornn et al (2012) proposed modeling non-stationarity through dimension expansion.…”

Section: Introductionmentioning

confidence: 99%

Non-Stationary Dependence Structures for Spatial Extremes

Huser

Genton

2016

JABES

View full text Add to dashboard Cite

Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable models have been developed, and fitted to various types of data. However, a recurrent problem is the modeling of non-stationarity. In this paper, we develop non-stationary max-stable dependence structures in which covariates can be easily incorporated. Inference is performed using pairwise likelihoods, and its performance is assessed by an extensive simulation study based on a non-stationary locally isotropic extremal t model. Evidence that unknown parameters are well estimated is provided, and estimation of spatial return level curves is discussed. The methodology is demonstrated with temperature maxima recorded over a complex topography. Models are shown to satisfactorily capture extremal dependence.

show abstract

Section: Introductionmentioning

confidence: 99%

Non-Stationary Dependence Structures for Spatial Extremes

Huser

Genton

2016

JABES

View full text Add to dashboard Cite

show abstract

“…In the case of stationary reducibility, several suggestions can be found in the literature, e.g. based on multidimensional scaling (Sampson and Guttorp, 1992), on radial basis deformation (Perrin and Monestiez, 1998), and on simulated annealing (Iovleff and Perrin, 2002). Research is currently underway on extensions of these techniques to locally stationary reducibility.…”

Section: Resultsmentioning

confidence: 99%

On a time deformation reducing nonstationary stochastic processes to local stationarity

Genton¹,

Perrin²

2004

Journal of Applied Probability

View full text Add to dashboard Cite

A stochastic process is locally stationary if its covariance function can be expressed as the product of a positive function multiplied by a stationary covariance. In this paper, we characterize nonstationary stochastic processes that can be reduced to local stationarity via a bijective deformation of the time index, and we give the form of this deformation under smoothness assumptions. This is an extension of the notion of stationary reducibility. We present several examples of nonstationary covariances that can be reduced to local stationarity. We also investigate the particular situation of exponentially convex reducibility, which can always be achieved for a certain class of separable nonstationary covariances.

show abstract

“…Sampson and Guttorp (1992) originally introduced the idea of using spatial deformations for nonstationary modeling. Since then, many authors have considered variations on this theme: space-time warping was considered by Meiring et al (1997) and Meiring et al (1998); Perrin and Monestiez (1998) introduced radial basis deformations to ensure bijectivity; Iovleff and Perrin (2004) discussed estimation via simulated annealing while Damian et al (2001) provided a Bayesian approach. Some authors have considered theoretical implications of deformation, Perrin and Meiring (1999) show the de- the bottom retain approximate stationarity.…”

Section: Nonstationary Simulationmentioning

confidence: 99%

High resolution simulation of nonstationary Gaussian random fields

Kleiber

2016

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

Simulation of random fields is a fundamental requirement for many spatial analyses. For small spatial networks, simulations can be produced using direct manipulations of the covariance matrix. Larger high resolution simulations are most easily available for stationary processes, where algorithms such as circulant embedding can be used to simulate a process at millions of locations. We discuss an approach to simulating high resolution nonstationary Gaussian processes that relies on generating a stationary random field followed by a nonlinear deformation to produce a nonstationary field. A spatially varying variance coefficient accounts for local scale effects. The nonstationary covariance function is estimated nonparametrically, and the deformation function is then estimated in a variational framework. We illustrate the proposed approach on synthetic datasets, a challenging temperature dataset over the state of Colorado and a regional climate model over North America.

show abstract

Modelling of Non-Stationary Spatial Structure Using Parametric Radial Basis Deformations

Cited by 26 publications

References 9 publications

Non-Stationary Dependence Structures for Spatial Extremes

Non-Stationary Dependence Structures for Spatial Extremes

On a time deformation reducing nonstationary stochastic processes to local stationarity

High resolution simulation of nonstationary Gaussian random fields

Contact Info

Product

Resources

About